Preprint 2003-002

Abstract:
This paper concerns a new lagrangian Discontinuous Galerkin type method to
solve 2D fluid flows on unstructured meshes. By using a basis of Bernstein
polynomials of degree $m$ in each triangle, we define a diffusion process
which ensures positivity and stability of the scheme. The discontinuities of
the physical variables at the interfaces between cells are solved with an
acoustic Riemann solver. A remeshing process is performed with a particle
method: this remeshing is locally conservative and its accuracy can be adapted
to the accuracy of the numerical method.